Looking for Great Grandfather John M Burke

Hello!

John M Burke, my great grandfather, was born in  Clonmel, Tipperary, Ireland on June 6, 1830.  He married Anna M Towhey in 1880  in the USA. She was his second wife. I do not know when he left Ireland, but it was before 1866, because he married his first wife here in the US that year.

John's first wife Ann (Murphy) was born in 1830 in County Lietrim, Parish Glenna (?).  They were married on May 1, 1866, in Nebraska City, Nebraska. Ann passed away on June 4, 1880, at age 50 in Nebraska City, Nebraska. She and John had no children.  

My great grandmother, Anna M Towhey (Touhey) born April 1, 1843 in County Mayo, came to the USA sometime between 1864 and 1871.  We believe she came with her sister Ellen, born in May of 1835.  The immigration dates are from US census records and vary. Their mother and father may have been named John and Ann.  

John married Anna Towhey (Touhey) in 1880. The 1885 Nebraska State Census lists John age 54, Ann age 34 and John 7 months, that would be John Francis, my grandfather.  The next record that I could find was the 1910 US census listing Anna M Burke as widowed living with John F (my grandfather) and Hattie W (Katherine Winifred) at 515 6th Corso in Nebraska City.  The census says Anna had three children, two living.  Their son Edward died at just 18 months old.  

John M Burke died on March 26, 1896, in Nebraska City, Nebraska USA, at the age of 65.  

My great-grandparents on my mother's side were were both born in Ireland and I am so happy to find this site so I might learn more about them!  I learned of this site from the watching Tar Abhaile.  I have been researching my family roots for over 30 years, but have just recently started using the internet. I often wonder what their lives were like in Ireland, what kind of work they did, and if we have relatives over there. I would like to know why they left Ireland, and more about the areas that they came from.